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<h1 class="reftitle">QuadFunction</h1>
<h2>Purpose</h2>
<p>Representation of quadratic functions in the form x'*H*x + F*x + g</p>
<h2>Syntax</h2>
<pre class="synopsis">Q = QuadFunction(H,F,g)</pre>
<pre class="synopsis">Q = QuadFunction(H,F)</pre>
<pre class="synopsis">Q = QuadFunction(H)</pre>
<pre class="synopsis">Q = QuadFunction(H,F,g,Data)</pre>
<h2>Description</h2>
<p></p>
        The <tt>QuadFunction</tt> class represents quadratic functions of the form <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction1.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction1.png"> 
        where <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction2.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction2.png"> is a real matrix, <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction3.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction3.png"> is a real matrix and <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction4.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction4.png">
        is a real column vector. Dimensions of <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction5.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction5.png">, <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction6.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction6.png"> and <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction7.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction7.png"> must coincide such that the output 
        is a scalar. 
        
	<h2>Input Arguments</h2>
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<td><tt>H</tt></td>
<td>
<p></p>Real matrix representing the coefficients in the quadratic term <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction8.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction8.png"> in  <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction9.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction9.png">.
        <p>
	    		Class: <tt>double</tt></p>
</td>
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<td><tt>F</tt></td>
<td>
<p></p>Real matrix representing the coefficients in the linear term <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction10.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction10.png"> in  <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction11.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction11.png">.
        <p>
	    		Class: <tt>double</tt></p>
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<td><tt>g</tt></td>
<td>
<p></p>Real vector representing the affine terms <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction12.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction12.png"> in  <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction13.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction13.png">.
        <p>
	    		Class: <tt>double</tt></p>
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<td><tt>Data</tt></td>
<td>
<p></p>Any data related to the function.
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<h2>Output Arguments</h2>
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<td><tt>Q</tt></td>
<td>
<p></p> 
         <tt>QuadFunction</tt> object. </td>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Construct a quadratic function <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction14.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction14.png"> 
      <pre class="programlisting">q1 = QuadFunction(1,0,1)</pre>
<pre class="programlisting">Quadratic Function: R^1 -&gt; R^1
</pre>Construct a quadratic function <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction15.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction15.png"> 
      <pre class="programlisting">q2 = QuadFunction(0.5,3,-1)</pre>
<pre class="programlisting">Quadratic Function: R^1 -&gt; R^1
</pre>
<h3>Example 
				2</h3>Construct a quadratic function <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction16.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction16.png">  where
                <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction17.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction17.png">, <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction18.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction18.png">, <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction19.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction19.png"> will be randomly generated and <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction20.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction20.png"> is a vector in dimension 2.
            <pre class="programlisting"> f = QuadFunction(randn(2),randn(1,2),randn(1)) </pre>
<pre class="programlisting">Quadratic Function: R^2 -&gt; R^1
</pre>
<h3>Example 
				3</h3> Construct quadratic function <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction21.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction21.png"> where <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction22.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction22.png">, <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction23.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction23.png"> and <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction24.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction24.png"> are regression coefficients from
        the data <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction25.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction25.png"> and <img src="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction26.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@QuadFunction/quadfunction26.png">.  The data we want to store <pre class="programlisting"> data.x = 0:0.01:0.5;</pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> data.y = cos(data.x);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> data.file= 'DSCa002';</pre>
<pre class="programlisting"></pre> Compute the regression coefficients and store them in <tt>h</tt>
      <pre class="programlisting"> h = polyfit(data.x,data.y,2); </pre>
<pre class="programlisting"></pre> We can store the data from which the function was obtained under <tt>Data</tt> property <pre class="programlisting"> QuadFunction(h(1),h(2),h(3),data)</pre>
<pre class="programlisting">Quadratic Function: R^1 -&gt; R^1
</pre>
<h2>See Also</h2>
<a href="../@Function/function.html">function</a>, <a href="../@AffFunction/afffunction.html">afffunction</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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